There are 32 crystallographic point groups. I have evaluated the symmetry elements of a few of them as examples of SymGen at work. Click the linked groups below to be shown a symmetry table for that group.
| triclinic | 1 |
|---|---|
| monoclinic | 2 m 2⁄m |
| orthorhombic | 222 mm2 mmm |
| tetragonal | 4 4/m 422 4mm 2m 4/mmm |
| trigonal | 3 32 3m m |
| hexagonal | 6 6⁄m 622 6mm 2m 6⁄mmm |
| cubic | 23 m 432 3m mm |